Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(\sin re \cdot 0.5\right) + e^{-im} \cdot \left(\sin re \cdot 0.5\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in0.0

    \[\leadsto \color{blue}{e^{0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)}\]

  4. Final simplification0.0

    \[\leadsto e^{im} \cdot \left(\sin re \cdot 0.5\right) + e^{-im} \cdot \left(\sin re \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2019004 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 22.2s)Debug log

sample366.0ms

Algorithm
intervals

simplify628.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

628.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
0.0b
(+ (exp (- 0 im)) (exp im))

rewrite46.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

27.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
17.0ms
(+ (exp (- 0 im)) (exp im))

series130.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

93.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
37.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.6s

Counts
19 → 38
Calls

19 calls. Slowest were:

312.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
310.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
285.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune391.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (exp im) (* 0.5 (sin re)))
0.0b
(* (exp (- 0 im)) (* 0.5 (sin re)))
0.0b
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
3 → 46
Calls

3 calls. Slowest were:

11.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
8.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
5.0ms
(* (exp im) (* 0.5 (sin re)))

series199.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

94.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
53.0ms
(* (exp im) (* 0.5 (sin re)))
51.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))

simplify2.6s

Counts
28 → 55
Calls

28 calls. Slowest were:

407.0ms
(* (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
386.0ms
(* (exp (* (exp (- 0 im)) (* 0.5 (sin re)))) (exp (* (exp im) (* 0.5 (sin re)))))
341.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))

prune525.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (+ (exp (- im)) (exp im)))
1.0b
(cbrt (+ (exp (- 0 im)) (exp im)))
1.0b
(cbrt (+ (exp (- 0 im)) (exp im)))
0.5b
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

39.0ms
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))
8.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
5.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))

series754.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

214.0ms
(cbrt (+ (exp (- im)) (exp im)))
191.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
176.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
173.0ms
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))

simplify4.0s

Counts
45 → 78
Calls

45 calls. Slowest were:

467.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im))))) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im))))))
302.0ms
(cbrt (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
269.0ms
(* (cbrt (+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))) (cbrt (- (exp (- 0 im)) (exp im))))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes267.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample9.1s

Algorithm
intervals